Isaac Newton Institute for Mathematical Sciences

Special Week on Quantum Cryptography

Quantum Correlations in Quantum Cryptography

Abstract

In basic quantum communication protocols one party creates quantum
states and uses a quantum channel to transmit it to another party that
performs immediately some measurement on it. This means, we effectively
create correlated (classical) data between distant parties. In order to
use the power of quantum mechanics, these correlation must show effects
of quantum mechanics.

In the specific example of quantum key distribution one uses the
correlations to distill a secret key in (classical) public discussion
protocols e.g. via sifting, error correction and privacy amplification.
We give a necessary condition for the success of any public discussion
protocol: the observed correlations should allow to prove the presence
of an internal, virtual state of entanglement in the distribution. This
poses a first test whether any presented real quantum key distribution
is indeed useful for the desired purpose. Moreover, a gap between the
parameter regime of proven security of given realistic schemes and the
regime of proven presence of vitual entanglement furthers the search for
the optimal public discussion protocol.